Puzzle time - Find the angle
-
wrote on 14 Oct 2020, 15:23 last edited by
Oh, I see. The relative size doesn't matter. It's always 120 degrees.
-
wrote on 14 Oct 2020, 15:34 last edited by
Can you prove it?
-
wrote on 14 Oct 2020, 15:53 last edited by Klaus
Well, I assume if I set up a formula for the angle given side length a and b for the triangles, then simplify using textbook identities for trigonometric functions, the a's and b's will magically cancel each other all out and I'll just get the 120 degrees.
There should be a tool online that turns geometric constructions into algebraic equations. There's pizza in the oven, so I can't be bothered to do that by hand right now
-
wrote on 14 Oct 2020, 15:56 last edited by
I'm going with 120 degrees.
My reasoning is that Klaus knows about this stuff.
-
wrote on 14 Oct 2020, 15:57 last edited by
Sorry, I should probably have put that in a spoiler
-
wrote on 14 Oct 2020, 16:50 last edited by
You can do it without complex trig identities. In your head in fact.
-
wrote on 14 Oct 2020, 18:56 last edited by
The sum of angles in the upper quadrilateral is 360 degrees. The top one must be 60 degrees. Beta and Gamma add up to 180 degrees. That leaves the desired 120 degrees. The only missing step is why beta and gamma add up to 180.
Something like that?
-
wrote on 14 Oct 2020, 18:58 last edited by
Not quite right but the solution is that ‘simple’.
-
wrote on 15 Oct 2020, 13:31 last edited by
My answer:
||
|| -
wrote on 15 Oct 2020, 14:11 last edited by Klaus
Nice! I'd add a little argument why the two angles you denote by theta are equal.
-
wrote on 16 Oct 2020, 04:23 last edited by
Ok. Angles 1 and 2 summed together obviously = 180 degrees, but then so do 2 and 3.
If 1+2=180, and 1+3=180, then 2=180-1 and 3=180-1 so 1 and 3 are equal.